(1) $\pi$ is the initial distribution of particle being at location $i$.
$\implies \pi(1) + \pi(2) + \pi(3) + … + \pi(n) = 1$
(2) (First Step) When particle is in location $i$, it can move to any position in {$1,2,…,i$} with uniform probability ie probability of particle going to location $k$ is $\frac{1}{i}$ where $k \le i$.
(3) (Second Step) When particle is in location $k$ after first step, it can move to any position in {$k,k+1,…,n$} with uniform probability ie probability of particle going to location $j$ is $\frac{1}{n-k+1}$ where $j \ge k$.
As given, after completing both steps, the final distribution of particle is uniform in {$1,2,…,n$} with probability that particle is in location $j$ is $\pi’(j) = \frac{1}{n}$.
$\therefore \pi’(1) = \frac{1}{n}$
Now, the probability in terms of $\pi(i)$ of particle being at location $1$ is given by –
$\pi’(1) = \pi(1) * \frac{1}{1} * \frac{1}{n} + \pi(2) * \frac{1}{2} * \frac{1}{n} + \pi(3) * \frac{1}{3} * \frac{1}{n} + … + \pi(n) * \frac{1}{n} * \frac{1}{n}$
$\implies \frac{1}{n} = \pi(1) * \frac{1}{1} * \frac{1}{n} + \pi(2) * \frac{1}{2} * \frac{1}{n} + \pi(3) * \frac{1}{3} * \frac{1}{n} + … + \pi(n) * \frac{1}{n} * \frac{1}{n}$
$\implies 1 = \pi(1) * \frac{1}{1} + \pi(2) * \frac{1}{2} + \pi(3) * \frac{1}{3} + … + \pi(n) * \frac{1}{n}$
$\therefore \pi(1) + \pi(2) + \pi(3) + … + \pi(n) = \pi(1) * \frac{1}{1} + \pi(2) * \frac{1}{2} + \pi(3) * \frac{1}{3} + … + \pi(n) * \frac{1}{n}$
$\implies \pi(2) + \pi(3) + … + \pi(n) = \frac{\pi(2) }{2} + \frac{\pi(3)}{3} + … + \frac{\pi(n)}{n}$
This is only possible when $\pi(2) = \pi(3) = … = \pi(n) = 0$
$\implies \pi(1) = 1 \text{ and } \pi(i) = 0, \forall i \neq 1$
Answer :- D.